Point Cluster Simplification Using Weighted Voronoi Diagram

This paper proposes an algorithm for simplifying point features on maps based on the multiplicatively weighted Voronoi diagram (MWVD). To ensure statistical, thematic, metric, and topological information contained in the original point features can be transmitted correctly after simplification, the algorithm selects corresponding measures to quantify these four types of information, and integrates the measures in the process of point feature generalization. First, the algorithm detects the range polygon of the given point features. Second, it adds the pseudo points to the original points to form a new point set and tessellates the new point set to get the MWVD. Third, it computes the selection probability of each point by means of the area of each Voronoi polygon, and sorts all points in descending order by their selection probability values. After this, it marks those will-be-deleted points as ‘deleted’ according to their selection probability values and their Voronoi neighboring relations, and determine if they can be physically deleted. Finally, the algorithm is ended by comparing the number of points retained on the map with that computed by the Radical Law. The algorithm is parameter free, automatic and easy to understand, owing to the use of the MWVD. As the experiments show, it can be used in the simplification of point features arranged in clusters such as thematic dot maps and control points on topographic maps. * Corresponding author